Theory Monad_Syntax

(*  Title:      HOL/Library/Monad_Syntax.thy
    Author:     Alexander Krauss, TU Muenchen
    Author:     Christian Sternagel, University of Innsbruck
*)

section Monad notation for arbitrary types

theory Monad_Syntax
  imports Adhoc_Overloading
begin

text 
We provide a convenient do-notation for monadic expressions well-known from Haskell.
const>Let› is printed specially in do-expressions.


consts
  bind :: "'a  ('b  'c)  'd" (infixl "" 54)

notation (ASCII)
  bind (infixl ">>=" 54)


abbreviation (do_notation)
  bind_do :: "'a  ('b  'c)  'd"
  where "bind_do  bind"

notation (output)
  bind_do (infixl "" 54)

notation (ASCII output)
  bind_do (infixl ">>=" 54)


nonterminal do_binds and do_bind
syntax
  "_do_block" :: "do_binds  'a" ("do {//(2  _)//}" [12] 62)
  "_do_bind"  :: "[pttrn, 'a]  do_bind" ("(2_ / _)" 13)
  "_do_let" :: "[pttrn, 'a]  do_bind" ("(2let _ =/ _)" [1000, 13] 13)
  "_do_then" :: "'a  do_bind" ("_" [14] 13)
  "_do_final" :: "'a  do_binds" ("_")
  "_do_cons" :: "[do_bind, do_binds]  do_binds" ("_;//_" [13, 12] 12)
  "_thenM" :: "['a, 'b]  'c" (infixl "" 54)

syntax (ASCII)
  "_do_bind" :: "[pttrn, 'a]  do_bind" ("(2_ <-/ _)" 13)
  "_thenM" :: "['a, 'b]  'c" (infixl ">>" 54)

translations
  "_do_block (_do_cons (_do_then t) (_do_final e))"
     "CONST bind_do t (λ_. e)"
  "_do_block (_do_cons (_do_bind p t) (_do_final e))"
     "CONST bind_do t (λp. e)"
  "_do_block (_do_cons (_do_let p t) bs)"
     "let p = t in _do_block bs"
  "_do_block (_do_cons b (_do_cons c cs))"
     "_do_block (_do_cons b (_do_final (_do_block (_do_cons c cs))))"
  "_do_cons (_do_let p t) (_do_final s)"
     "_do_final (let p = t in s)"
  "_do_block (_do_final e)"  "e"
  "(m  n)"  "(m  (λ_. n))"

adhoc_overloading
  bind Set.bind Predicate.bind Option.bind List.bind

end